## Why Japanese Multiplication Works

Japanese Multiplication? Chinese Multiplication? Line Multiplication? Whatever it’s called, it’s only a trick if you simply memorize without meaning   Have you ever wondered why Japanese multiplication works? I’ve heard some call it Chinese multiplication,...

## Counting Principles – Counting and Cardinality

A Progression of Counting and Quantity Success in mathematics begins with the development of a sense of number through counting and quantity. It may seem that children learn to count in much the same way that they learn their alphabet – by simply repeating...

## The Progression of Fractions

Exploring Fraction Constructs and Proportional Reasoning Fractions are a beast of a concept that causes struggles for many adults and students alike. While we all come to school with some intuition to help us with thinking fractionally and proportionally, the...

## The Progression of Multiplication

Arrays and Area Models to The Standard Algorithm Did you know that the words “array” and “area model” appear in the Grade 1-8 Math Curriculum a combined 22 times? Not only do arrays and area models help to support the development of...

## The Progression of Proportional Reasoning From K-9

The Foundation and Development of Multiplicative Thinking Proportional Reasoning is a big idea that is connected in some way to all mathematical strands and stretches across many grades in the Ontario mathematics curriculum. While many focus on the importance of...

## Visualizing Proportional Reasoning: Working With Ratios and Proportions

Solving Proportions With The Toronto Maple Leafs Win:Loss Ratio As we began the Proportional Reasoning unit in my MFM1P Grade 9 Math Course, I was beginning to struggle with an idea to extend the idea of visualizing mathematics concepts into ratios, rates, and...